Utility companies generate electrical power, often at many hundred thousand volt levels, and distribute the power over a reconfigurable grid system to various customer loads. Conservative system design requires anticipation of the many contingent modes of failure that may occur in such a system. It is understood that a fault contingency is a sequence of events, the first of which is usually (but need not be) a fault, for example a falling tree severing a power-carrying line. For example, if a generator fails to output sufficient power, the defective generator must be taken off-line to remove the fault condition. Next, the grid is reconfigured so customers formerly supplied electricity from the failed generator can receive power from another generator. Of course many other faults can also contribute to a system failure.
Any of these failure modes, and others as well, may lead to fault conditions that can damage the distribution system, perhaps catastrophically, and/or can cause great inconvenience to the customer. In each instance, once the defective system components are identified and taken off-line, a post-fault system equilibrium condition is attained and analyzed. A decision is then made whether it is necessary to reconfigure the grid in a given fashion to continue to supply electricity, to the best of available resources.
But once post-fault equilibrium condition is reached, the grid may be reconfigured in a great number of ways, some of which will be more optimum than others. Further, determining the best reconfiguration of the remaining system may have to be accomplished within a matter of minutes. The problem then is how to best determine an optimum system reconfiguration in a finite amount of time.
Most prior art dynamic security analysis techniques assume that predicting system security with respect to a given contingency, requires a knowledge of (a) the post-fault equilibrium condition, (b) severity of the disturbance as given by system state deviation system immediately after fault-clearing from post-fault equilibrium, and (c) system ability to withstand the disturbance as given by the maximum potential energy at the relevant unstable equilibrium point of the post-fault system. Although attempts have been made to use these quantities to develop a severity index to quickly rank and screen contingencies, including variants of the transient energy function ("TEF"), computational inefficiency resulted.
The prior art approach requires computation of the post-fault equilibrium, a potentially complex computation. Although some contingencies may be harmless, the prior art approach does not permit a simple screening out of such contingencies. In essence, the prior art attempts to capture the dynamic state of the system with a single index, with which index contingencies may be precisely ranked. However, this approach is extremely computational intensive and may require many hours of calculation before a meaningful decision can be derived. However, during the rather lengthy analysis period, the grid cannot be intelligently reconfigured.
It is known in the art to attempt to employ neural networks in the power system security field to form a continuous input/output model of non-linear systems, as a classifier. Less commonly, such networks are employed as a decision tree with learned criteria. Artificial neural network methodology is based on developing models of elementary processing units. Simple local connection strength modulation procedures are formulated such that the strengths are adjusted to reflect complex input/output relationships, wherein each neural network node is a processing element. In a simple back-propagation implementation, each node sums a collection of weighted inputs, and passes the result to its output through a non-linear transformation function. This function could be a relay or a saturation along with a threshold value, a sigmoid function, or other similar function. When the non-linearity is a relay, the resulting output merely is a classification of the input as belonging to one or the other of the two half-spaces formed by a hyper-plane in the space of the input variables.
Those skilled in the art recognize that a typical neural network requires training before actual use, with training occurring in a supervised training mode or in an unsupervised training mode.
Supervised training of neural networks includes identifying the weights associated with the inputs at each node for a given set of threshold values. This is accomplished by first selecting the threshold values for each node and the initial values for the weights. A set of training inputs is then presented to the network, and the output is compared to the desired outputs. The error at the output of each node is used to modify the weights appropriately, e.g., by simple rules and known algorithms. Suitable algorithms are described in the Proceedings of the IEEE, September and October 1990, Special Issue of Neural Networks, I Theory and Modeling, and II Analysis, Techniques and Applications. The selected set of training inputs are presented again and again until the output errors are within the required tolerance. The quality of the results of the neural network depends on the quality of the selected topology, the values of the thresholds, and the training data.
Unsupervised neural network training may be done in two methods. The first method is similar to that of associative memories, where the neural network automatically divides the input samples into appropriate clusters. Kohonen networks are a good example of such classifiers. In the second method, some of the connections between the nodes act as feedbacks from the outputs of nodes at a later level, with outputs of the nodes oscillating until settling down to an equilibrium points. Such networks are known as Hopfield networks.
Unfortunately, dimensionality-associated problems have precluded the successful use of neural networks in the assessment of power system security. For example, M. A. El-Sharkaswi et al., Proceedings of the Second Symposium on Expert Systems Application to Power Systems, Univ. of Washington, Seattle, Jul. 17-20, 1989, p. 366-370 attempted a dynamic security assessment of a three generator power system using an artificial neural network. The fifteen-neuron network identified the operating region wherein the real part of all eigenvalues were negative, but over 400 training sets were required before the neural network would perform satisfactorily.
Another experimenter, Y. H. Pao, IEEE Trans. on Power Systems, Vol. 4, No. 1, February 1989, used a seven-neuron Rumelhart feed-forward net with an error back-propagation learning scheme to predict the critical fault clearing time ("CCT") of a power system having 4 generators and 7 lines. Thirty twelve-dimensional training sets were obtained using two different topologies (full system and one line outaged) and 15 different loading levels. The desired training mode output were the CCTs for a fault at a prescribed bus. The neural network was able to predict the CCTs for different loading levels with remarkable accuracy, both for the two topologies used in the training sets, as well as a new topology where a different line was outaged. However, this performance was achieved after presenting the training set to the network 5010 times.
H. Mori et al., Proceedings of PICA, May 7-10, 1991, Baltimore, p. 293-301, used an unsupervised competitive learning scheme based on the Kohonen Model. Mori et al. presented 5000 operating conditions of a 3 generator, 9 bus, 9 line system to a neural net acting as a self-organizing feature mapping system. The 5000 training cases were mapped automatically into a two dimensional square grid of 900 cells.
Yet another attempt reported by Y. H. Pao et al., Proceedings of PICA, May 7-10, 1991, Baltimore, p. 278-284 used a combination of unsupervised and supervised learning schemes. These experimenters considered a 4 generator, 6 bus, 6 line system using 138 training patterns (of 20 features each) for three different topologies. The unsupervised training process classified these patterns into 13 clusters, wherein for each cluster, a supervised training procedure calculated the critical fault clearing time (CCT) using only one neuron for each cluster.
These prior art approaches have a number of characteristics in common in that they all considered small system models, wherein the employed methodology could not readily be easily extended to a practical sized system. Further, in these approaches, the size of the neural network was a function of the system size in that increasing system size would drastically increase the required processing time. Further, prior art techniques make no clear definition of neural network inputs or the type of outputs from the neural network.
What is needed is a more rapid method for dynamically ranking contingencies following a fault in a power distribution system. Such method should result in a practical cal on-line dynamic security analysis system that can deal with realistic power system models comprising thousands of buses and hundreds of generators. Preferably such method should provide meaningful and objective benchmark guidance as to reconfiguring the grid within minutes rather than hours of a fault condition. Further, the analytical methodology should be independent of the complexity of the system under analysis.
The present invention discloses such a method.